# Questions tagged [wolfram-alpha]

For mathematical questions related to the usage of WolframAlpha.

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### Analysis of a deceptively simple infinite product: $f(n) = \prod_{j=2}^{\infty}\left(1-\frac{1}{j^n}\right)$

I am reading the book "An introduction to Infinite Product" by Charles H. C. Little , Kee L. Teo and Bruce van Brunt (https://doi.org/10.1007/978-3-030-90646-7). The book mentions the ...
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### Why does a product $\lim_{n\to\infty} \prod_{i=1}^n (1- \frac{1}{n+2i})$ lead to infinity?

I asked Wolfram Alpha to compute the following limit: $\lim_{n\to\infty} \prod_{i=1}^n (1- \frac{1}{n+2i})$ and the answer was $\infty$. I do not understand how this can be, as all elements in the ...
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### Why won't Wolfram Alpha compute my Limit? [closed]

Wolfram input: ...
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### Why does Wolfram Alpha give two different, inconsistent answers for sum of a matrix?

I would like to find out what $\sum_{r=1}^{n} \pmatrix{1 & -1 \\ 0 & 2}^r$ is equal to. I have typed this expression into WolramAlpha twice and got a different answer each time, both ...
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### Steps WA used to simplify $\left( \frac{\cos \beta \sin \beta \cos\phi +\sin \beta}{\sin^2 \phi + \sin^2\beta \cos^2 \phi} \right)^2\cos \phi$

I have the following expression: $$\left( \frac{\cos \beta \sin \beta \cos\phi +\sin \beta}{\sin^2 \phi + \sin^2\beta \cos^2 \phi} \right)^2\cos \phi$$ Wolfram Alpha yields a simplified form of this ...
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### Why does Wolfram Alpha give a wrong answer to a linear ODE with constant coefficients?

This is very odd as it is a really simple ODE and the interpretation of the input seems correct, yet Wolfram Alpha produces rubbish: $$x'' - 2x' + x = t, \quad x(0) = 1.$$ Wolfram Alpha claims that ...
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### How does Wolfram find the closed form of numbers?

Introduction I don't know if this question has already been asked (I didn't find it in the list of questions already asked) and I hope it won't be closed immediately since it's technically a question ...
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### How to integrate to get sinh? (Wolfram Alpha)

I am currently trying to find the curve that a surfer makes in attempting to get to beyond where the waves break while a current pushes against him perpendicularly, and am using this post as help: ...
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### Plot a piece of a spherical shell - Wolfram Alpha website

I'd like to know how to plot a piece of a spherical shell $0.118<r<0.236$, $0<\theta<\pi$, $0<\phi<\pi/2$ by using the website Wolfram Alpha.
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1 vote
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### How to obtain a recurrence relation for Taylor series coefficients?

Recently, I asked WolframAlpha to give me the first few terms in the Taylor series for a complicated (but well-behaved) function. It did so, but also provided a recurrence relation for the ...
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### Value of $x$ such that the area under the curve of $lnx$ up to $x$ is $1$.

This value would be the solution to:$$\int_{0}^{a}\ln(x)dx=1$$ With integration by parts this is well known to be $[x\ln(x)-x]^a_0=1$ or what is the same:$$a\ln(a)-a=1$$ The limit at $0$ easily ...
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### Wolfram Mathematica: why is the plot not visible?

simple question regarding Wolfram Mathematica: Why is the plot not showing? (See screenshot) (I am new to Wolfram Mathematica) Thankful for any input.
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1 vote
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### How are person curves created?

One can graph some person curves such as Joe Biden curve and Kim Jung Un Curve using WolframAlpha. I am curious how these curves were created using parametric equations.
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